Projections, Extendability of Operators and the Gateaux Derivative of the Norm

1995 ◽  
Vol 1 (1) ◽  
Author(s):  
L. Gajek ◽  
J. Jachymski ◽  
D. Zagrodny
Keyword(s):  
Gâteaux Derivative ◽  
Gateaux Derivative

scholarly journals The Gâteaux derivative and orthogonality in C∞

2012 ◽  
Vol 20 (1) ◽  
pp. 275-284
Author(s):  
Salah Mecheri ◽  
Hacene Mecheri
Keyword(s):  
Banach Space ◽  
General Problem ◽  
Operator Theory ◽  
Differential Analysis ◽  
Generalized Derivations ◽  
Global Minima ◽  
Gâteaux Derivative ◽  
Affine Mappings ◽  
Elementary Operators ◽  
Gateaux Derivative

Abstract The general problem in this paper is minimizing the C∞− norm of suitable affine mappings from B(H) to C∞, using convex and differential analysis (Gateaux derivative) as well as input from operator theory. The mappings considered generalize the so-called elementary operators and in particular the generalized derivations, which are of great interest by themselves. The main results obtained characterize global minima in terms of (Banach space) orthogonality.

scholarly journals GATEAUX and FRÉCHET DERIVATIVE IN INTUITIONISTIC FUZZY NORMED LINEAR SPACES

2012 ◽  
Vol 08 (03) ◽  
pp. 311-322 ◽  
Author(s):  
BIVAS DINDA ◽  
T. K. SAMANTA ◽  
U. K. BERA
Keyword(s):  
Fréchet Derivative ◽  
Linear Spaces ◽  
Gâteaux Derivative ◽  
Frechet Derivative ◽  
Normed Linear Spaces ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Derivative ◽  
Gateaux Derivative

In this paper, we introduce intuitionistic fuzzy derivative, intuitionistic fuzzy Gateaux derivative and intuitionistic fuzzy Fréchet derivative and some of their properties are studied. The relations between intuitionistic fuzzy Gateaux derivative and intuitionistic fuzzy Fréchet derivative are studied.

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